SKF BSS Ground ball screws

Transcription

1 SKF BSS Ground ball screws

2 Contents The SKF brand now stands for more than ever before, and means more to you as a valued customer. While SKF maintains its leadership as the hallmark of quality bearings throughout the world, new dimensions in technical advances, product support and services have evolved SKF into a truly solutions-oriented supplier, creating greater value for customers. These solutions encompass ways to bring greater productivity to customers, not only with breakthrough application-specific products, but also through leading-edge design simulation tools and consultancy services, plant asset efficiency maintenance programmes, and the industry s most advanced supply management techniques. The SKF brand still stands for the very best in rolling bearings, but it now stands for much more. SKF the knowledge engineering company 1 General Recommendations... 4 Selection... 4 Basic dynamic load rating... 4 Static load carrying capacity... 5 Critical rotating speed for screw shafts... 5 Permissible speed limit... 5 Efficiency and back-driving... 6 Axial play and preload... 6 Static axial stiffness of a complete assembly... 7 Screw shaft buckling... 7 Manufacturing precision... 8 Materials and heat treatments... 8 Number of circuits of balls... 8 Assembly procedure... 9 Radial and moment loads... 9 Alignment... 9 Lubrication... 9 Designing the screw shaft ends... 9 Starting-up the screw... 9 Operating temperature Technical data Lead precision according to ISO Geometric tolerance Design and functional specifications Geometric profile of the track/ball area Preload Materials and thermal expansions Checking of the maximum axial operating load Application of precision ball screw Product information Ordering key PGFJ Flanged nut with internal preload, DIN standard PGFL Double preloaded flanged nut long lead PGFE Double preloaded flanged nut PGCL Cylindrical double preloaded nut Standard end machined End bearings Product Inspection and certification How to orientate your choice Calculation formulas SKF - the knowledge engineering company

3 General 1 SKF BSS SKF Bss, to accomplish its overall set of goal, has take part of the 75 years tradition of Gamfior, the precision mechanical manufacturing Italian company. Sharing knowledge and highly qualified experience, is the SKF way of stay in front of the increasingly fast technical-production developments of the market. To inherit the Italian company, as an integral part of its organisation, represents in fact a further step of SKF s improving processes in the technical high precision production of ball screws. This Italian business unit (or division) comprises buildings and departments covering sq. mts. The production environment, plunged in a plantation of about a thousand conifers, reflects the SKF responsibility of it s human resources offering safe and good working conditions. In effect SKF is committed to creating an environment where the skill and experience of the operator is decisive, side by side with foreman NC machines, computers systems and CAD systems. The most significant aspect of that Italian b.u. is the integrated development of the production, including its mechanical and electronic components, which provides the ideal basis for contacts with the customer. 3

4 2 Recommendations Selection Recommendations Selection NB.: Only basic selection parameters are included. To make the very best selection of a ball screw, the designer should specify such critical parameters as the load profile, the linear or rotational speed, the rates of acceleration and deceleration, the cycle rate, the environment, the required life, the lead accuracy, the stiffness, and any other special requirement. If in doubt, please consult an SKF ball screw specialist before placing an order. Basic dynamic load rating (C a ) The dynamic rating is used to compute the fatigue life of ball screws. It is the axial load constant in magnitude and direction, and acting centrally under which the nominal life (as defined by ISO) reaches one million revolutions. Nominal fatigue life L 10 The nominal life of a ball screw is the number of revolutions (or the number of operating hours at a given constant speed) which the ball screw is capable of enduring before the first sign of fatigue (flaking, spalling) occurs on one of the rolling surfaces. It is however evident from both laboratory tests and practical experience that seemingly identical ball screws operating under identical conditions have different lives, hence the notion of nominal life. It is, in accordance with ISO definition, the life achieved or exceeded by 90 % of a sufficiently large group of apparently identical ball screws, working in identical conditions (alignment, axial and centrally applied load, speed, acceleration, lubrication, temperature and cleanliness). Service life The actual life achieved by a specific ball screw before it fails is known as service life. Failure is generally by wear, not by fatigue (flaking or spalling); wear of the recirculation system, corrosion, contamination, and, more generally, by loss of the functional characteristics required by the application. Experience acquired with similar applications will help to select the proper screw to obtain the required service life. One must also take into account structural require ments such as the strength of screw ends and nut attachments, due to the loads applied on these elements in service. Equivalent dynamic loads The loads acting on the screw can be calculated according to the laws of mechanics if the external forces (e.g. power transmission, work, rotary and linear inertia forces) are known or can be calculated. It is necessary to calcu late the equivalent dynamic load: this load is defined as that hypothetical load, constant in magnitude and direction, acting axially and centrally on the screw which, if applied, would have the same influence on the screw life as the actual loads to which the screw is subjected. Radial and moment loads must be taken by linear bearing systems. It is extremely important to resolve these problems at the earliest conceptual stage. These forces are detrimental to the life and the expected performance of the screw. Fluctuating load When the load fluctuates during the working cycle, it is necessary to calculate the equivalent dynamic load: this load is defined as that hypothetical load, constant in magnitude and direction, acting axially and centrally on the screw which, if applied, would have the same influence on the screw life as the actual loads to which the screw is subjected. Additional loads due, for example to misalignment, uneven loading, shocks, and so on, must be taken in account. Their influence on the nominal life of the screw is generally taken care of, consult SKF for advice. 4

5 Static load carrying capacity (C oa ) Critical rotating speed for screw shafts Permissible speed limit Ball screws should be selected on the basis of the basic static load rating C oa instead of on bearing life when they are submitted to continuous or inter mit tent shock loads, while stationary or rotating at very low speed for short duration. The permissible load is deter mined by the permanent deformation caused by the load acting at the contact points. It is defined by ISO standards as the purely axially and centrally applied static load which will create, by calculation, a total (rolling element + thread surface) permanent deformation equal to 0,0001 of the diameter of the rolling element. A ball screw must be selected by its basic static load rating which must be, at least, equal to the product of the maximum axial static load applied and a safety factor so. The safety factor is selected in relation with past experience of similar applications and requirements of running smoothness and noise level (1). The shaft is equated to a cylinder, the diameter of which is the root diameter of the thread. The formulas use a parameter the value of which is dictated by the mounting of the screw shaft (whether it is simply supported or fixed). As a rule the nut is not considered as a support of the screw shaft. Because of the potential inaccuracies in the mounting of the screw assembly, a safety factor of. 80 is applied to the calculated critical speeds. Calculations which consider the nut as a support of the shaft, or reduce the safety factor, require practical tests and possibly an optimization of the design (1). The permissible speed limit is that speed which a screw cannot reliably exceed at any time. It is generally the limiting speed of the recirculation system in the nut. It is expressed as the product of the rpm and the nominal diameter of the screw shaft (in mm). The speed limits quoted in this catalogue are the maximum speeds that may be applied through very short periods and in optimized running conditions of alignment, light external load and preload with monitored lubri cation. Running a screw continuously at the permissible speed limit may lead to a reduction of the calculated life of the nut mechanism. The lubrication of screws rotating at high speed must be properly considered in quantity and quality. The volume, spread and frequency of the application of the lubricant (oil or grease) must be properly selected and monitored). At high speed the lubricant spread on the surface of the screw shaft may be thrown off by centrifugal forces. It is important to monitor this phenomenon during the first run at high speed and possibly adapt the frequency of relubrication or the flow of lubricant, or select a lubricant with a different viscosity. Monitoring the steady temperature reached by the nut permits the frequency of relubrication or the oil flow rate to be optimized. 2 (1) SKF can help you to define this value in relation with the actual conditions of service. ATTENTION!: High speed associated with high load requires a large input torque and yields a relatively short nominal life (1). In the case of high acceleration and deceleration, it is recommended to either work under a nominal external load or to apply a light preload to the nut to avoid internal sliding during reversal. The value of preload of screws submitted to high velocity must be that preload which ensures that the rolling elements do not slide (1). Too high a preload will create unacceptable increases of the internal temperature. 5

6 2 Recommendations Selection Efficiency and back-driving The performance of a screw is mainly dependant on the geometry of the contact surfaces and their finish as well as the helix angle of the thread. It is, also, dependant on the working conditions of the screw (load, speed, lubrication, preload, alignment, etc ). The direct efficiency is used to define the input torque required to transform the rotation of one member into the translation of the other. Conversely, the indirect efficiency is used to define the axial load required to transform the translation of one member into the rotation of the other one. It is used, also, to define the braking torque required to prevent that rotation. It is safe to consider that these screws are reversible or back-driveable under almost all circumstances. It is therefore necessary to design a brake mechanism if backdriving is to be avoided (gear reducers or brake). Preload torque: Internally preloaded screws exhibit a torque due to this preload. This persists even when they are not externally loaded. Preload torque is measured at 100 rpm (without wipers) when assembly is lubricated with ISO grade 68 oil. Starting torque: This is defined as the torque needed to overcome the following to start rotation: a) the total inertia of all moving parts accelerated by the energy source (including rotation and linear movement). b) the internal friction of the screw/nut assembly, bearing and associated guiding devices. In general, torque to overcome inertia (a) is greater than friction torque (b). The coefficient of friction of the high efficiency screw when starting μs is estimated at up to double the dynamic coefficient μ, under normal conditions of use. Axial play and preload Preloaded nuts are subject to much less elastic deformation than non-preloaded nuts. Therefore they should be used whenever the accuracy of positioning under load is important. Preload is that force applied to a set of two half nuts to either press them together or push them apart with the purpose of eliminating backlash or increasing the rigidity or stiffness of the assembly. The preload is defined by the value of the preload torque (see under that heading in the previous paragrah). The torque depends on the type of nut and on the mode of preload (elastic or rigid). Preload systems Lead + Shift Fig. 1 Nut PGFJ Lead Lead Screw Nut Lead Lead QGFL QGFE QGCL Screw Nut Nut Lead Lead PGFE PGCL Screw 6

7 Static axial stiffness of a complete assembly It is the ratio of the external axial load applied to the system and the axial displacement of the face of the nut in relation with the fixed (anchored) end of the screw shaft. The inverse of the rigidity of the total system is equal to the sum of all the inverses of the rigidity of each of the components (screw shaft, nut as mounted on the shaft, supporting bearing, supporting housings, etc ). Because of this, the rigidity of the total system is always less than the smallest individual rigidity. Nut rigidity When a preload is applied to a nut, firstly, the internal play is eliminated, then, the Hertzian elastic deformation increases as the preload is applied so that the overall rigidity increases. The theoretical deformation does not take into account machining inaccuracies, actual sharing of the load between the different contact surfaces, the elasticity of the nut and of the screw shaft. The practical stiffness values given in the catalogue are lower than the theoretical values for this reason. The rigidity values given in the SKF ball screw catalogue are individual practical values for the assembled nut. They are determined by SKF based on the value of the selected basic preload and an external load equal to twice this preload. Elastic deformation of screw shaft This deformation is proportional to its length and inversely proportional to the square of the root diameter. According to the relative importance of the screw deformation (see rigidity of the total system), too large an increase in the preload of the nut and supporting bearings yields a limited increase of rigidity and notably increases the preload torque and therefore the running temperature. Consequently, the preload stated in the catalogue for each dimension is optimum and should not be increased. Screw shaft buckling The column loading of the screw shaft must be checked when it is submitted to compression loading (whether dynamically or statically). The maximum permissible compressive load is calculated using the Euler formulas. It is then multiplied by a safety factor of 3 to 5, depending on the application. The type of end mounting of the shaft is critical to select the proper coefficients to be used in the Euler formulas. When the screw shaft comprises a single diameter, the root diameter is used for the calculation. When the screw comprises different sections with various diameters, calculations becomes more complex (1). 2 (1) SKF can help you to define this value in relation with the actual conditions of service. 7

8 2 Recommendations Selection Manufacturing precision Generally speaking, the precision indication given in the designation defines the lead precisions see page 11 lead precision according to ISO (ex. G5 - G3 ). Parameters other than lead precision correspond to our internal standards (generally based on ISO class 5). If you require special tolerances (for example class 5) please specify when requesting a quotation or ordering. Materials and heat treatments Standard screw shafts are machined from steel which is surface hardened by induction (C48 or equivalent). Standard nuts are machined in steel which is carburized and through hardened (18 Ni CrMo5 or equivalent). Hardness of the contact surfaces is HRc, depending on diameter, for standard screws. Number of circuits of balls A nut is defined by the number of ball turns which support the load. The number is changing, according to the product and the combination diameter/lead. It is defined by the number of circuits and their type. Working environment Our products have not been developed for use in an explosive atmosphere, consequently we cannot take any responsability for the use in this field. 8

9 Assembly procedure Note.: Ground ball screws are precision components and should be handled with care to avoid shocks. When stored out of the shipping crate they must lie on wooden or plastic vee blocks and should not be allowed to sag. Screw assemblies are shipped, wrapped in a heavy gauge plastic tube which protects them from foreign material and possible pollution. They should stay wrapped until they are used. 2 Radial and moment loads Any radial or moment load on the nut will overload some of the contact surfaces, thus significantly reducing its life. Alignment SKF linear guidance components should be used to ensure correct alignment and avoid non-axial loading. The parallelism of the screw shaft with the guiding devices must be checked. If external linear guidance prove impractical, we suggest mounting the nut on trunnions or gimbals and the screw shaft in selfaligning bearings. Mounting the screw in tension helps align it properly and eliminates bucking. Lubrication Good lubrication is essential for the proper functioning of the screw and for its long term reliability (1). Before shipping, the screw is coated with a protective fluid that dries to a film. This protective film is not a lubricant. Depending on the selected lubricant, it may be necessary to remove this film before applying the lubricant (there may be a risk of non-compatibility). If this operation is performed in a potentially polluted atmosphere it is highly recommended to proceed with a thorough cleaning of the assembly. Designing the screw shaft ends Generally speaking, when the ends of the screw shaft are specified by the customer s engineering personnel, it is their responsability to check the strength of these ends. However, we offer in pages 16 and 17 of this catalogue, a choice of standard machined ends. As far as possible, we recommend their use. Whatever your choice may be, please keep in mind that no dimension on the shaft ends can exceed do (otherwise traces of the root of thread will appear or the shaft must be made by joining 2 pieces). A minimum shoulder should be sufficient to maintain the internal bearing. Starting-up the screw After the assembly has been cleaned, mounted and lubricated, it is recommended that the nut is allowed to make several full strokes at low speed; to check the proper positioning of the limit switches or reversing mechanism before applying the full load and the full speed. Operating temperature Screws made from standard steel and operating under normal loads can sustain temperatures in the range 10 C + 70 C. Above 70 C, materials adapted to the temperature of the application should be selected. Consult SKF for advice. Note: Operating at high temperature will lower the hardness of the steel, alter the accuracy of the thread and may increase the oxidability of the materials. 9

10 3 Technical data Technical data Lead precision according to ISO Lead precision is measured at 20 C on the useful stroke l u, which is the threaded length decreased, at each end, by the length l e equal to the screw shaft diameter see ( table 1) and ( fig. 1). Table 1 Fig. 1 G1 G3 G5 V300p, μm l u e p v up e p v up e p v up mm μm μm μm (315) (400) (500) (630) (800) (1000) (1250) (1600) (2000) (2500) (3150) l u = useful travel l e = excess travel (no lead precision required) l o = nominal travel l s = specified travel c = travel compensation (difference between ls and lo to be defined by the customer, for instance to compensate an expansion) Case with value of c specified by the customer e p = tolerance over the specified travel V = travel variation (or permissible band width) V 300p = maximum permitted travel variation over 300 mm V up = maximum permitted travel variation over the useful travel lu V 300a = measured travel variation over 300 mm V ua = measured travel variation over the useful travel Case with c = 0 = standard version in case of no value given by the customer le Threaded lengt h l u μm + l e Fig. 2 Threaded lengt h μm + Fig. 3 mm l 0 l e l u l e v up e p c v up e p l 0 mm e p e p l m - l s - 10

11 Geometric tolerances Run-out tolerances ( table 2) Tolerances tighter than the currently applicable ISO/TC39/WG7 specifications and the Internal Draft Standard ISO/DIS ( fig. 4). The division into ISO accuracy classes ISO 1 ( table 3), ISO 3 ( table 4), ISO 5 ( table 5) and ISO 7 ( table 6) refers, however, to these standards. 3 Fig. 4 t 10 A B t 1 t 3 t 4 AB C C t 6 AB D f t 7 AB t 2 t 5 AB D t 9 A B d 1 D 1 L o L o L n 2d 1 2d 1 2d 1 L n L o C A A 2d 1 t 8 A B B B D Run-out tolerances - Maximum permissible deviations Table 2 Position t 1 t 2 Radial run-out of the diameter of bearing seat in relation to reference supports Position t 3 t 4 t 5 Radial run-out of the diameter of the end of the screw in relation to bearings seats Position t 6 t 7 Axial run-out of the faces of the bearing seat in relation to reference supports Position t 9 Radial run-out of the location diameter of the nut in relation to the reference supports Position t 10 Deviation of the parallelism of the mounting surfaces of the nut in relation to the reference supports Position t 11 Radial run-out of the free ends with rigidity blocked nut Position t 8 Axial run-out of the ball nut location face in relation to the reference supports 11

12 3 Technical data Geometric tolerances ISO 1 - Dimensions in mm Table 3 Position t 1 t 2 d 1 L n Tolerance ,005 0, ,029 0,048 t = L n 0, ,048 0, ,010 0, ,024 0, ,040 0,080 Position t 6 - t 9 Position t 8 t = L n 0, d 1 Tolerance D f Tolerance Position t 3 t 4 t 5 d 1 L 0 Tolerance ,002 0, ,005 0,010 t = L 0 0, ,010 0, ,002 0, ,004 0,008 t = L 0 0, ,008 0,012 Position t 9 Position t 10 D 1 Tolerance Tolerance , , , , , , ,016 0, ,020 ISO 3 - Dimensions in mm Table 4 Position t 1 t 2 d 1 L n Tolerance ,005 0, ,038 0,064 t = L n 0, ,064 0, ,012 0, ,030 0,050 t = L n 0, ,050 0, Position t 6 t 7 Position t 8 d 1 Tolerance D f Tolerance Position t 3 t 4 t 5 d 1 L 0 Tolerance ,003 0, ,006 0,012 t = L 0 0, ,012 0, ,003 0, ,005 0,010 t = L 0 0, ,010 0,015 Position t 9 Position t 10 D 1 Tolerance Tolerance , , , , , , ,020 0, ,025 ISO 5 - Dimensions in mm Table 5 Position t 1 t 2 d 1 L n Tolerance ,010 0, ,060 0,100 t = L n 0, ,100 0, ,020 0, ,048 0,080 t = L n 0, ,080 0,160 Position t 6 t 7 Position t 8 d 1 Tolerance D f Tolerance Position t 3 t 4 t 5 d 1 L 0 Tolerance ,004 0, ,008 0,016 t = L 0 0, ,016 0, ,003 0, ,006 0,012 t = L 0 0, ,012 0,018 Position t 9 Position t 10 D 1 Tolerance Tolerance , , , , , , ,025 0, ,032 12

13 ISO 7 - Dimensions in mm Table 6 Position t 1 t 2 d 1 L n Tolerance ,020 0, ,120 0,200 t = L n 0, ,200 0, ,040 0, ,094 0,157 t = L n 0, ,157 0,315 Position t 6 t 7 Position t 8 d 1 Tolerance D f Tolerance Position t 3 t 4 t 5 d 1 L 0 Tolerance ,006 0, ,012 0,025 t = L 0 0, ,025 0, ,005 0, ,010 0,020 t = L 0 0, ,020 0,030 Position t 9 Position t 10 D 1 Tolerance Tolerance , , , , , , ,032 0, ,040 Radial run-out of the free ends with rigidly blocked nut d 1 t 11 M measurement length L m M Table 7 For ISO d 1 L m Tolerance t ,005 0, ,010 0, ,006 0, ,012 0, ,010 0, ,018 0,055 13

14 3 Technical data Design and functional specifications Design and functional specifications Geometric profile of the track/ball area Ball/track contact pressures and, therefore, axial load capacity are optimized through in depth study of the profile of the groove consisting of two gothic arcs that are in a specific ratio to the radius of the ball D W /2, so as to generate the optimal contact angle α ( fig. 5). According to the direction of the load, the ball/track contact points are at B or A.The displacement Δa of the ball from point A to point B is the effective axial play of the ball screw. Under stationary conditions, the radial play Δr of the system is related to this. Preload Two nuts are used forced apart according to a preload force at rest F pr in order to enhance positioning accuracy, eliminating axial and rad al play, and to improve system rigidity. Application of an external load F A increases the load and deformation on nut 2 to the values F (2) and Δl b/t(2) while nut 1 is detensioned to the same extent. When the Fig. 5 external load reaches the value F l = 2,83 F pr, the preload is eliminated (condition of no play), ( diagram 1). Figure 6 and diagram 2 show the different behaviour of nuts preloaded or with play. The optimal preload depends on a wide range of application parameters and must be purpose-designed for more harsher uses. SKF BSS recommends an optimal preload of maximum 12 % of the basic dynamic axial load rating C am. Preload must be defined according to the load applied and the required rigidity. With external loads F A, the preload value that Diagram 1 B A D w/2 1 2 Δa 1 2 Δr Deformation of nut 1 Δl b/ta Deformation of nut 2 r s r n Fl 1 2 Δr 1 2 Δa A d 1 screw outer diameter B d 0 nominal diameter lead angle (= Dp w pitch circle diameter) Axial load FA Δl b/t(2) Δl b/t(1) F A F (2) F pr F (1) Lead P h = π d 0 tan Δl b/tpr Δl b/tpr Nut 2 Nut 1 Diagram 2 Fig. 6 parallel lines Fl = 2,83 F pr preloaded nut nut with play Δl b/t propor tional to F A 2/3 Nut 2 Preload force F pr Nut 1 F N F N Axial load FA F p Δl b/tpr 2Δl b/tpr F N External load F A F N Elastic def ormation Δl b/t 14

15 ensures conditions of no play is, as seen above, equal to F A /2,83. Once the ball screw has been dimensioned with the calculated required rigidity, a further increase n the preload does not lead to any very noticeable increase in rigidity ( fig. 7) but tends to reduce ball screw life due to the increase in the operating torque and in temperature. Each time the temperature increases by one degree above 20 C, there is an approx. 0,01 mm elongation per degree and per meter in the steel used to construct the precision ball screw. Preloading systems In addition to the above-mentioned system, in which two preloaded nuts are used, the single preloaded nut system can be applied by using larger-sized balls (with four contact points) or with a shift in the lead of the nut tracks. Permissible deviations for the preload torque (ISO/DIS Draft Standard) table 8 gives the maximum permis sible tolerance values ± ΔT pp in % in relation to the nominal torque T po ; the effective values T pa and ±ΔT pa measured with the procedure outlined in the paragraph above must be within this range. Materials and thermal expansions SKF BSS ball screw shafts are made of particularly impuretyfree steels, able to withstand the heat treat ments applied without cracking or uncontrolled defor - mations. The track-ball contact area is surfacehardened by applying strictly controlled induction hardening proce dures for the screw shafts and case hardening pro cedures for the nuts followed by deep freeze treat - ment (for the residual austenite) and soft tempering. Constant hardening thicknesses of 2 mm are thus obtained with hardness values of HRC. The ends of the screws are usually hardened and tempered (R = dan/mm 2 ). The thermal expansion coefficient of the screw is K a = /degree; the resulting axial elongation at a thermal gradient of Δθ [ C] is therefore: 3 Δl = K a Δθ L [mm] This should be taken into account when selecting the correct preload and lead compensation in order to obtain optimal working conditions. Fig. 7 F D 1 Table 8 ΔT pp (% of T p0 ) T p0 [Nm] L u /d 0 < 40; L u < 4000 mm L u /d 0 < 60; L u < 4000 mm L u > 4000 mm from to ISO 1 ISO 3 ISO 5 ISO 7 ISO 1 ISO 3 ISO 5 ISO 7 ISO 1 ISO 3 ISO 5 ISO 7 0,2 0, ,4 0, , , ,5 6, ,

16 3 Technical data Design and functional specifications Checking of the maximum axial operating load ln low speed applications and generally speaking in all applications with high axial loads, F MAX greater than the mean load F m, even for short periods, it is advisable to make a static check on possible permanent deforma tions generated at the ball/track contact. Referring to the definition of C oa and C oam, the static load safety coefficient f s is calculated: f s = C oam F MAX which must be kept within the following values: f s = 1 1,5 regular operation without vibrations 1,5 2 normal operation with limited vibrations 2 3 strong shock loads and vibrations 3 4 very smooth operating requirements For compressive axial loads, this check must be made together with calculation of the maximum permissible column load. 16

17 Application of precision ball screw Lubrication Oil Lubrication of precision ball screws has many similarities with lubrication of ball bearings, so that similar products are used. However, the conditions of accuracy in which ball screws must operate do not permit any noticeable increases in temperature; there - fore, where the application allows, it is advisable to use oil lubrication which helps to disperse the heat in the track/ball contact area. Generally, the same oils are used as for ball bearings with optimal viscosity calcu lated according to the geometry, speed and operating temperature. The viscosity grade ISO VG [mm 2 /s or Cst at 40 C] in conformity with DIN standard can be obtained from ( Diagram 3) according to screw shaft diameter, average speed and operating temperature for the application concerned. The amount of oil required also depends on the application conditions; an oil volume of 2 5 cm 3 /h is usually prescribed for each ball turn (1 impulse every 5 30 min). In case of oil-immersed horizontal screws, the level of lubricant must reach the axis of the lowest ball. In case of applications with operating conditions other than normal, oils can be used with special additives to improve stability and anti-corrosion charac teristics. Grease In low speed operating conditions, waterresistant greases are usually used according to grade 2 DIN Greasing should be repeated for machine tools every 2-3 months in the initial operating phase and 6 10 months subsequently. The amount of grease used must fill approximately half of the available internal space. Greases with a different saponifying content must never be mixed. Under exceptional circumstances of use, such as high speed or heavy loads, it is advisable to use greases conforming to DIN prescriptions, type NLGI and NLGI 3. For specific lubrication SKF should be consulted for advices. Protective covers SKF BSS standard precision ball screws are supplied complete with plastic wiper rings which prevent leak age of lubricant and penetration of external impurities. Special seals for applications in particularly dirty or contaminated environments can be designed case by case on request. A bellows or telescopic type protec tion is always useful in these cases. 3 Diagramm 3 Mean equivalent speed n m [rpm] Oil viscosity ISO VG [mm 2 /sec at 40 C] Screw outer diameter d 1 [mm] Operating temperature [ C] 17

18 4 Product information Product information Ordering key Nut type: Nut with internal preload, DIN standard PGFJ Double preloaded flanged nut PGFL Double preloaded flanged nut, DIN PGFE Cylindrical double preloaded nut PGCL Nut with axial play SGFL Nut with axial play, DIN SGFE Cylindrical nut with axial play SGCL Four contact preloded flanged nut QGFL Four contact preloded flanged nut, DIN QGFE Cylindrical four contact preloded nut QGCL Nominal diameter Lead [mm] Hand: Right R Left (on request) L Number of circuits of balls Threaded length / Total length [mm] Lead precision: G5, G3, G1 Nut orientation: Threaded side or flange of nut towards shorter (S) or longer (L) machined end of shaft. In case of same end machining ( ) Machined end combination to customer's drawing PGFE / WPR Wipers: Always with wipers WPR Example: PGFE 32 5 R / 445 G1 L HA +K WPR Axial static stiffness of the nut Table 1 Actual stiffness = theoretical stiffness x accuracy factor Accuracy factor* 0,6 0,55 0,5 0,4 ISO Accuracy classes *Accuracy factor takes into account the effect on stiffness of dimensional errors, surface finish, nut/ball/screw shaft coupling during construction and assembly of the screw as a function of the ISO precision class Note: In case L-HA+K of Z (to customer s drawing) please, always send a readable DWG. 18

19 PGFJ - Flanged nut with internal preload, DIN standard 4 Designation Screw Lead Number of Basic load ratings Preload Nut d 2 D J Design D 5 D 1 A A 3 A 2 L 8 diam- circuits of dynamic static torque stiffness eter balls d 0 P h C a C oa T pe R n* mm mm kn kn Nm N/μm mm mm mm mm mm mm mm mm mm PGFJ ,7 14,2 0, , , PGFJ ,4 24,5 0, , , PGFJ ,6 33,6 0, , , PGFJ ,2 39,5 0, , , PGFJ ,1 57 0, , PGFJ ,2 80 0, , PGFJ ,6 73 0, , PGFJ , , , PGFJ , , , PGFJ , , PGFJ ,2 93 0, , PGFJ , , PGFJ , , , PGFJ , , PGFJ , , PGFJ , , , PGFJ , , , PGFJ , , PGFJ , , , PGFJ , , , * See table 1 page 22 Options: Balls in ceramic material Rotating nut 19

20 4 Product information PGFL - Double preloaded flanged nut long lead M M8 1 for size after Designation Screw Lead Number of Basic load ratings Preload Nut d 2 D J D5 D 1 A A s A 3 A 2 diam- circuits of dynamic static torque stiffness Dble Sgle eter balls nut nut d 0 P h C a C oa T pe R n** mm mm kn kn Nm N/μm mm mm mm mm mm mm mm mm mm PGFL ,75 20,5 43 0, , , PGFL ,75 20,5 43 0, , , PGFL 32 20* , , , PGFL 32 25* , , , PGFL 32 32* ,75 19,5 41,8 0, , PGFL ,75 30,9 68,4 0, , PGFL ,8 36,5 72,8 0, , PGFL , , * Brush wipers & n d0 < ** See table 1 page 22 Note: Nut is available with axial play SGFL, nut length will be A s or with contact points preload QGFL. Options: Balls in ceramic material Rotating nut 20

21 PGFE - Double preloaded flanged nut, DIN 4 Designation Screw Lead Numb. of Basic load Preload Nut d 2 D J Design D 5 D 1 A As A 3 A 2 L 8 diam- circuits ratings torque stiff- Dble Sgle eter of balls dynamic static ness nut nut d 0 P h C a C oa T pe R n* mm mm kn kn Nm N/μm mm mm mm mm mm mm mm mm mm mm PGFE ,7 14,2 0, , , , PGFE ,4 24,5 0, , , , PGFE ,8 23 0, , , PGFE ,4 35 0, , , PGFE ,6 33,6 0, , , PGFE ,7 40,5 0, , , PGFE ,2 39,5 0, , , PGFE ,5 48 0, , , PGFE ,3 42,8 0, , PGFE ,1 57 0, , PGFE ,3 52,5 0, , PGFE ,5 62 0, , PGFE ,2 80 0, , PGFE ,6 73 0, , PGFE ,1 89 0, , PGFE , , PGFE ,5 98 0, , PGFE , , , PGFE , , , PGFE , , PGFE , , PGFE ,5 95 0, PGFE ,4 0, , PGFE ,6 89,1 0, , Continued ** See table 1 page 22 Note: Nut is available with axial play SGFE, nut length will be A s or with contact points preload QGFE. Options: Balls in ceramic material Rotating nut 21

22 4 Product information PGFE (Continued) Designation Screw Lead Numb. of Basic load Preload Nut d 2 D J Design D 5 D 1 A A s A 3 A 2 L 8 diam- circuits ratings torque stiff- Dble Sgle eter of balls dynamic static ness nut nut d 0 P h C a C oa T pe R n* mm mm kn kn Nm N/μm mm mm mm mm mm mm mm mm mm mm PGFE ,2 93 0, , PGFE , , PGFE , , PGFE , , , PGFE , , , PGFE , , PGFE , , , PGFE , , PGFE , , PGFE , , , PGFE , , PGFE , , , PGFE , , PGFE , , PGFE , , , PGFE , , PGFE , , PGFE , , , PGFE , , , PGFE , , , PGFE , , , PGFE , , , PGFE , , , PGFE , , PGFE , , PGFE , , , PGFE , , , * See table 1 page 22 Note: Nut is available with axial play SGFE, nut length will be A s or with contact points preload QGFE. Continued Options: Balls in ceramic material Rotating nut 22

23 PGFE (Continued) 4 Designation Screw Lead Numb. of Basic load Preload Nut d 2 D J Design D 5 D 1 A A s A 3 A 2 L 8 diam- circuits ratings torque stiff- Dble Sgle eter of balls dynamic static ness nut nut d 0 P h C a C oa T pe R n* mm mm kn kn Nm N/μm mm mm mm mm mm mm mm mm mm mm PGFE , , , PGFE , , , PGFE , , , PGFE , , , PGFE , , PGFE , , , PGFE , , , PGFE , , , , PGFE , , , PGFE , , , PGFE , PGFE , , , PGFE , , , PGFE , , , PGFE , , , * See table 1 page 22 Note: Nut is available with axial play SGFE, nut length will be A s or with contact points preload QGFE. Options: Balls in ceramic material Rotating nut 23

24 4 Product information PGCL - Cylindrical double preloaded nut Designation Screw Lead Numb. of Basic load ratings Preload Nut d 2 D Keyway A A s A 11 Lub. diam- circuits dynamic static torque stiffness Dble Sgle diameter eter of balls nut nut Q d 0 P h C a C oa T pe R n* mm mm kn kn Nm N/μm mm mm mm mm mm mm mm PGCL ,7 14,2 0, , , ,5 30,2 3 PGCL ,4 24,5 0, , , ,5 30,2 3 PGCL ,8 23 0, , , ,5 PGCL ,4 35 0, , , ,5 PGCL ,6 33,6 0, , , PGCL ,7 40,5 0, , , ,5 4 PGCL ,2 39,5 0, , , ,7 4 PGCL ,5 48 0, , , ,5 PGCL ,3 42,8 0, , , PGCL ,1 57 0, , , PGCL ,3 52,5 0, , , ,5 4 PGCL ,5 62 0, , , ,5 4,5 PGCL ,2 80 0, , , ,2 PGCL ,6 73 0, , , PGCL ,8 66,9 0, , , ,5 4 PGCL ,1 89 0, , , ,5 4 PGCL , , , ,5 4,5 PGCL ,5 98 0, , , ,2 PGCL , , , , ,2 PGCL , , , , ,5 7 PGCL , , , ,6 7 PGCL ,2 93 0, , , PGCL , , , PGCL , , , ,2 PGCL , , , ,5 6,2 PGCL , , , , PGCL , , , , * See table 1 page 22 Note: Nut is available with axial play SGCL, nut length will be A s or with contact points preload QGCL. Continued Options: Balls in ceramic material Rotating nut 24

25 PGCL (Continued) Options: Balls in ceramic material Rotating nut 4 Designation Screw Lead Numb. of Basic load ratings Preload Nut d 2 D Keyway A A s A 11 Lub. diam- circuits dynamic static torque stiffness Dble Sgle diameter eter of balls nut nut Q d 0 P h C a C oa T pe R n* mm kn Nm N/μm mm PGCL , , , ,5 3 PGCL , , , ,5 3 PGCL , , , ,2 PGCL , , ,2 PGCL , , PGCL , ,5 9,5 PGCL , ,5 9,5 PGCL , , ,2 PGCL , , ,2 PGCL , , ,5 7 PGCL , ,5 PGCL , , ,5 PGCL , , ,5 12,5 PGCL , , ,5 12,5 PGCL , , ,2 PGCL , , ,2 PGCL , , ,5 7 PGCL , , PGCL , ,5 PGCL , , ,5 PGCL , , ,5 12,5 PGCL , , , ,5 12,5 PGCL , , ,5 7 PGCL , , PGCL ,5 PGCL , , ,5 PGCL , , ,5 12,5 PGCL , , ,5 12,5 * See table 1 page 22 25

26 4 Product information Standard end machined Standard end machining for nominal diameter 16 mm Standard shaft ends for ball screws, nominal diameter 16 mm, have been developed to suit the SKF thrust bearings. These standard ends are the same for all screw types. Dimensions (mm) Size d 5 d 4 d 10 d 11 d 12 B 1 B 2 B 3 B 4 B 5 B 6 B 7 B 9 d 8 G G1 m d 6 c c 1 d 0 h7 h6 h6 h7 js12 js12 js12 H11 js12 6g +0,14 h11 5) +0 h12 6) b a d 7 r a Keyway to DIN 6885 a N9 xi xb h11 fixed end free end (type 2A) (type 5A) / ,5 M10 0, ,1 9,6 0,5 0,5 1,2 8,8 0,4 A A / ,5 M ,1 9,6 0,5 0,5 1,5 10,5 0,8 A A ,4 7) / , M ,1 16,2 0,5 0,5 1,5 15,5 0,8 A A ,4 7) / ,5 0 21,7 M ,1 16,2 0,5 0,5 1,5 18,5 1,2 A A ,8 7) / ,5 67 4,5 0 33,5 M30 1,5 25 1,6 28,6 1 0,5 2,3 27,8 0,8 A A ,4 7) / ,5 67 4,5 0 35,5 M35 1,5 27 1,6 28,6 1 0,5 2,3 32,8 1,2 A A ,8 7) / , M50 1,5 32 1,85 42,5 1,5 1 2,3 47,8 1,2 A A ,8 7) / , M ,85 42,5 1, ,1 1,6 A A ,8 7) 5) For screw d o 16 to d o 32; 6) For screw d o 40 to d o 63; 7) For ends 4A or 5A; 0 No shoulder; / No shoulder Shaft end combinations Ø 16 mm Order code Two machined ends AA (without cut only length indication) BA 1A + 2A FA* 2A + 2A GA* 2A + 3A HA 2A + 4A JA 2A + 5A MA 3A + 5A SA (+ length) Ends to root diameter d 2, any possible lengths. UA (+ length) End machined to diameter d 3 under induction hardening, any possible lengths. K Z Keyway To customer's drawing * Attention! This mounting requires the greatest precautions. Please contact us. 26

27 Standard machined ends for nominal diameter 16 mm Threaded length = total length - end length 1A 2A 3A d 4 G d 5 d 4 G d 0 R a c x 45 c x 45 r a c x 45 b a x d 7 G 1 B 1 (B 2 ) G 1 b a x d 7 B 4 B 1 4A 5A Keyway B 7 x d 8 B 5 B 7 x d 8 B 5 m x d 6 4 m x d 6 d 11 d 12 d 11 a N 9 r a c 1 x 45 r a B 3 c x 45 c x 45 B 3 c x 45 B 6 (B 10 ) c x 45 End length End bearings A special design for a specific application High-precision Single Direction Angular Contact Thrust Ball Bearings have been developed especially for the support of ball and roller screws in machine tools. They incorporate a large number of balls and have a special internal design with a contact angle of 60 to provide superior axial stiffness. These bearings also have high axial load ratings, high running accuracy together with speed and acceleration capability and low frictional torque. Ready to mount units To simplify and speed up mounting, complete greased-for-life cartridge units are available in matched sets of two, three or four Single Direction Angular Contact Thrust Ball Bearings in a flanged housing. These units are sealed and due to the flange can be simply bolted to the machine frame. Double Direction Angular Contact Thrust Ball Bearings with and without integrated flange, sealed and greased for life are also a part of the product range. Note: For other informations on the products please consult SKF BSS. 27

28 4 Product information Product inspection and certification Final certification of standard testing The certificate of conformity gives the geometric parameters measured and compared with SKF BSS specifications as set forth on pages above. The radial run-out of the free ends of the screw with the ball nut rigidly fixed can also be certified. Final certification of special inspection provided on request a Measuring and plotting of the dynamic preload drag torque according to ISO/DIS specifications or according to special customer requests ( fig. 1). b Measuring and plotting of actual travel variation compared with permissible value, using computer controlled laser systems ( fig. 2). c Measuring and plotting of nut axial rigidity according to ISO/DIS specifications ( fig. 3). d The very low speed rotation torque can be measured and plotted, if specifically requested, in order to assess the stickslip of the ball screw. SKF BSS code SKF BSS 28

29 SKF BSS T ORINO - IT AL Y Scre w Diameter 40 mm B ALL SCREWS RIGIDITY CAR TIFICA TE A CCURA CY CLASS ISO 3 Lead 5 mm Ball Diameter 3, 5 m m Customer Customer dra wing Required Rigidity 90/ 150 dan/ μ m SKF BSS code VS Serial No PR ODUCT INSPECTIO N No / 2586 Date 05/03/ Preload F pr F 1 = 0,5 x F pr F 2 = 2 x F pr Δλ 1 = 1,004 μ m Δλ 2 = 3,889 μ m are the sum of the elasti c def or mations in the two directions caused respecti ve ly by the axial loads ±F e 1 ±F 2 Rigidity in the range ±F dan 50 dan 200 dan F [ dan ] F 1 R nu1 = = Δλ 1 99,6 dan/ μ m Rigidity in the range +F 1 to +F 2 and -F 1 to -F 2 2(F 2 -F 1 ) R nu2 = = Δλ 2 - Δλ 1 104,0 dan/ μ m 30 Def or mation D λ [ μ m ] SKF BSS code SKF BSS 29

30 4 Product information This catalogue concerns only ground ball screws. However, a ground ball screw may not meet all the demands of your application; in this case choose a roller screw as roller screws perform beyond the limits of ball screws. How to orientate your choice Fig. 1 Fig. 2 In our wide range, you are sure to find the product which fits exactly your requirements: The miniature ball screws ( fig. 1), either with ball recirculation by integrated tube or with inserts, are very compact. Backdriving makes them highly efficient. The rolled screws ( fig. 2) enable you to select the right level of requirement: simple transport screws, very fast screws with long lead, or preloaded screws for more precision. Ground ball screws for more rigidity and precision ( fig. 3). High load capacity ball screws with BIG BALLS ( fig. 4) for moulding injection, punching, bending press machines and direct hydraulic cylinder replacements. Roller screws ( fig. 5) which are far beyond the limits of any ball screws as for heavy loads, ultimate precision and rigidity, high speed and acceleration and very difficult environments. Fig. 3 Fig. 4 Table 1 will guide you in your first approach. Fig. 5 30

31 Table 1 Type Details Basic dynamic Precision High duty Adverse load rating Ep (μ) on 300 mm cycles environment (Spec. steel, pollution) SH series Diameter Ø 6 to 16 mm Up to 5,2 kn G9 (130 μ) good to G5 (23 μ) SX, SL/TL, SN/TN/PN Din standard Up to 80 kn G9 (130 μ) satisfactory Ø 16 to 63 mm to G5 (23 μ) PGFJ, PGFL, PGFE, PGCL Ø 16 to 125 mm Up to 270 kn G5 (23 μ) satisfactory to G1 (6 μ) 4 SGFH, Ø 50 to 125 mm Up to 850 kn G5 (23 μ) exceptional to G1 (6 μ) SRC, SRF, TRK/PRK, SVC, PVK Up to 2235 kn G5 (23 μ) exceptional Ø 8 to 210 mm to G1 (6 μ) 31

32 4 Product information Calculation formulas Calculation formulas 1 Dynamic load rating (N) and Basic life rating L 10 = C a 3 F m or C req = F m (L 10 ) 1/3 req L 10 = life (milion of revolutions) C a = basic dynamic load rating C req = required dynamic load rating F m = cubic mean load [N] 2 Cubic mean load (N) F m = (F 1 3 L 1 +F 2 3 L 2 +F 3 3 L 3 + ) 1/3 (L 1 + L 2 + L 3 + ) 1/3 F m = F min + 2F max (L 1 + L 2 +L 3 + ) 1/3 3 Critical speed of screw shaft (rpm) (no safety factor) (a factor of 0,8 is generally recommended) n cr = f 1 d 2 2 l 2 d 2 = root diameter [mm] l = free lenght, or distance between the two support bearings f 1 = 0,9 fixed, free 3,8 fixed, supported 5,6 fixed, fixed 4 Speed limit of the mechanism (maxi speed applied through very short periods - to be confirmed, depending on the application) For instance: n d 0 < , to the exception of long leads: 32 20/25/ and 63 50: n d 0 < , if higher, please consult SKF n = revolutions per minute d 0 = screw shaft nominal diameter 5 Buckling strength (N) (with a safety factor: 3) F c = f 2 d 2 4 l 2 d 2 = root diameter [mm] l = free length, or distance between the two support bearings f 2 = mounting correction factor 0,25 fixed, free A 1 supported, supported B 2 fixed, supported C 4 fixed, fixed D 32

33 6 Deflection of the screw shaft due to its own weight (mm) p l 4 Δl rad = K p E Ι Distributed weight P [dan/mm] Δl rad E = [dan/mm 2 ] I = Π d 2 4 [mm 4 ] 64 = 1/8 in configuration A (fixed/free) Dl rad on the free end = 5/384 in configuration B (supported/supported) Dl rad on the centreline K p = 1/185 in configuration C (fixed/supported) Dl rad at 0,42 L from the simple support = 1/384 in configuration D (fixed/free) Dl rad on the centreline Intermediate supports that reduce the above deflection can be used in very long applications. 7 Rigidity The total rigidity of a screw is: 1 R t R t = F δ = R s R n F = load δ = deflection R s = screw shaft rigidity R n = nut rigidity 4 The rigidity of a screw shaft is: Ball screw held rigidity at one end: 2 d 2 R s = 165 [Nμm] Ι for standard steel Ball screw held rigidity at both ends: 165 d 22 Ι R s = Ι 2 (Ι Ι 2 ) for standard steel 8 Theoretical efficiency direct (η) η= K d 0 P h K = 0,00974 d 0 = nominal diameter of screw shaft P h = lead [mm] indirect (η') η' = 2 1 η 9 Pratical efficiency (η p ) η p = η 0,9 The value 0,9 used is an averange value betwen the practical efficiency of a new screw and that of a properly run in screw. It should be used for industrial applications in all normal working conditions. For extreme cases, call us. 33

34 4 Product information Calculation formulas 10 Input torque in a steady state (Nm) F = maximum load of the cycle [N] F P h T = π η p 11 Power required in a steady state (W) n = revolution per minute F n P h P = η p 12 Preload torque (Nm) Fpr= preload force between a nut and the F pr P h T pr = η shaft [N] π Restraining torque (Nm) (considering system backdriving) T B = F P h η' π F = load [N] For safety, we can use the theoretical indirect efficiency 14 Nominal motor torque when accelerating (Nm) 15 Nominal braking torque when decelerating (Nm) For a horizontal screw T t = T f + T pr + P h [F + m L μ f g] π η p +ω Ι For a vertical screw T t = T f + T pr + P h [F + m L g] π η p +ω Ι For a horizontal screw T' t = T f + T pr + P h η' [F + m L μ f g] π For a vertical screw T t = T f + T pr + P h η' [F + m L g] 200 π +ω Ι +ω Ι T f = torque from friction in support bearings [Nm] T pr = preload torque [Nm] μ f = coefficient of friction η p = real direct efficiency ω = angular acceleration [rad /s 2 ] m L = mass of the load [kg] g = acceleration of gravity: 9,8 [m/s 2 ] Ι = Ι M + Ι L + Ι S + Ι 10 9 [kg/m 2 ] Ι L = m L P h 2π [kg m 2 ] η' = theoretical direct efficiency Ι M = inertia of motor [kg m 2 ] Ι S = inertia of screw shaft per metre [kg mm 2 /m] Note: For additional information, please contact SKF. 34

35 Symbols C req N Required load rating C a kn The dynamic load rating (L10 life) is such that 90 % of a sufficiently large sample of identical screws can be expected to attain or exceed 1 million revolutions under this constant centrally acting pure axial load without fatigue (flaking). C oa kn The static load rating is that axial constant centrally acting load which produces a total permanent deformation of one raceway and roller of 0,0001 of the diameter of the curved surface of the roller. F N Axial load F c N Compression load F m N Constant mean axial load F pr N The preload force between a nut half (or nut) and the shaft F q N The squeeze load applied to two nut halves (or nuts) by the housing or fixing bolts Hv - Vickers hardness I kgm 2 Inertia I L kgm 2 Inertia of load I M kgm 2 Inertia of motor I nn kgm 2 Inertia of nut when turning nut I ns kgm 2 Inertia of rollers when turning shaft I s kgmm 2 /m Inertia of screw shaft per metre L 10 6 revs Life L revs Basic life rating, millions of revolutions L 10h hours Basic life rating, operating hours M μm Maximum difference between mean travels of screws in a matched set N - Number of thread starts on the screw shaft N r - Standard number of rollers N max - Maximum number of rollers P watts Power P h mm Lead R N/μm Rigidity R n N/μm Nut rigidity y including deflection of: R ng N/μm Minimum guaranteed nut rigidity s the nut body s rollers / nut contact s rollers / screw shaft s contact R nr N/μm Reference nut rigidity s length of screw shaft b in contact with rollers R s N/μm Screw shaft rigidity R t N/μm Total rigidity T Nm Torque T B Nm Brake torque T dt Nm Total torque at constant speed T f Nm Torque from friction in support bearings, motor, seals, etc T pe Nm Torque for play elimination T pr Nm Preload torque T st Nm Starting torque T t Nm Total torque U mm Stroke length y V hr -1 Strokes per hour W hr/day Hours per day X days/year Days per year Y years Years Z s cc Grease quantity for screw shaft Z n cc Grease quantity for nut s s life calculation s b c μm Travel compensation - the difference between the specified travel and the nominal travel. Its value is always defined by the customer: if not specified it will be assumed to be zero. (The specified travel can also be defined by the specified lead multiplied by the number of revolutions) d o mm Nominal y d 1 mm Outside d 2 mm Root d b mm Bore s diameter of screw shaft s b e p μm Tolerance of actual mean travel, l m relative to specified travel l s f - Factors g m/s 2 Acceleration of gravity: 9,8 l mm Length l o mm Nominal travel - the nominal lead multiplied by the number of revolutions l 1 mm Threaded length l e mm Excess travel - at each end of the threaded length a distance le is subtracted to leave l u the useful travel. The specified lead precision does not apply to the lengths l e. l u = l 1-2 l e l m mm Actual mean travel. The curve is the result of measurements at 20 C of the screw shaft. l m is the line which fits the curve by the method of least squares l s mm Specified travel l tp mm Maximum total length l u mm Useful travel - the length of thread which is subject to the specifi ed lead precision m kg Mass m L kg Mass of the load m n kg Mass of the nut m s kg/m Mass of the screw shaft per metre n rpm Rotational speed n cr rpm Critical speed n p rpm Maximum permissible speed s ap mm Maximum axial play t μm Manufacturing tolerance v μm Travel variation - the band width or the distance between the two straight lines parallel to the actual mean travel which enclose the curve v 300 μm The bandwidth over any 300 mm section of the useful travel. v 300a and v 300p are actual and permissible values v u μm The bandwidth over the useful travel. v ua and v up are actual and permissible values d μm Deflection a Helix angle of the screw shaft thread l Friction angle y tan l = μ μ Coefficient of friction b μ st Coefficient of friction when starting μ F Coefficient of friction for bearing s Mpa Nominal axial stress s p Mpa Real axial stress s t Mpa Total stress t Mpa Nominal shear stress t p Mpa Real shear stress h Theoretical direct efficiency h Theoretical indirect efficiency h p Real direct effi ciency h p Real indirect effi ciency q Angle of twist w rad/s 2 Angular acceleration W mm rpm Speed quotient, n p d o 4 35

36 36

37 37

38 Notes 38

39

40 Contact SKF BSS Represented by: SKF is a registered tredemark of SKF SKF 2007 The contents of this publication are the copyright of the publisher and may not be reproduced (even extracts) unless permission is granted. Every care has been taken to ensure the accuracy of information contained in this publication but no liability can can be accepted for any loss or damage whether direct, indirect or consequential arising out of the use of the information contained herein. Publication 4621/1 EN Printed in Italy